A Multilevel Approach for Obtaining Locally Optimal Finite Element Meshes

In this paper we consider the adaptive finite element solution of a general class of variational problems using a combination of node insertion, node movement and edge swapping. The adaptive strategy that is proposed is based upon the construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and connectivity of the nodes is optimized. This grid is then locally refined and the new mesh is optimized in the same manner. Results presented indicate that this approach is able to produce better meshes than those possible by more conventional adaptive strategies and in a relatively efficient manner.